Spin Polarization through Floquet Resonances in a Driven Central Spin Model

Adiabatically varying the driving frequency of a periodically driven many-body quantum system can induce controlled transitions between resonant eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic transitions in the Floquet spectrum and presenting a general tool in quantum many-body control. Using the central spin model as an application, we show how such controlled driving processes can lead to a polarization-based decoupling of the central spin from its decoherence-inducing environment at resonance. While it is generally impossible to obtain the exact Floquet Hamiltonian in driven interacting systems, we exploit the integrability of the central spin model to show how techniques from quantum quenches can be used to explicitly construct the Floquet Hamiltonian in a restricted many-body basis and model Floquet resonances.

Figure 1

Phase spectrum of the Floquet operator, quasienergies, and dynamical energies for a periodically driven central spin Hamiltonian at different driving periods $T$. The dotted (blue) lines mark the edges of the Brillouin zone $\pm \pi ({\theta }_n)$ and $\pm \pi /T$ $({\theta }_n/T)$, while the vertical dotted line denotes $T_c=2\pi /W$. The ground state and highest excited state are highlighted red using the approximative results from integrability (see below).

Figure 2

Expectation values of $H_{\mathrm{av}}$ and $S_0^z$ with respect to the adiabatic ground state of the Floquet Hamiltonian when the driving period is slowly increased from $0.8T_c$ to $1.2T_c$ (first column) or from $1.8T_c$ to $2.2T_c$ (second column) with $T_{i+1}-T_i={10}^{-4}$. Blue lines are exact results, while the red line is the approximation from integrability (see below). The dashed lines indicate the spectrum of $H_{\mathrm{av}}$.

Figure 3

Expectation value of the time-averaged Hamiltonian in the adiabatic ground state of the Floquet Hamiltonian with driving $B_z=1\pm 0.2$ and $\eta =1/2$ for different system sizes $L$.

Figure 4

Magnetization of the central spin in the adiabatic ground state of the Floquet Hamiltonian at different driving periods with $L=25$ and driving $B_z={\overline{B}}_z\pm 0.2$.